Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1

Berrou, Claude; Glavieux, Alain; Thitimajshima, Punya

doi:10.1109/icc.1993.397441

Cited by 5,817 publications

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“…A typical turbo code (TC) was first introduced in 1993 by Berrou et al, [1] as a class of near channel capacity achieving codes. This turbo code is constructed by concatenating two parallel convolutional codes via an interleaver as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…2 summarizes this interleaver design dependence criteria. A Random interleaver in [1] utilized in turbo codes performs reasonable for long block sizes. However, for short block size, the performance of turbo codes with a random interleaver degrades substantially even it performs worse than that of convolutional codes with similar computational complexity.…”

Section: Introductionmentioning

confidence: 99%

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The Design of New Modified Block and Matched S-Random Interleavers for Turbo Codes

Soliman¹,

Yang²,

Ejaz³

2014

IJMO

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Abstract-It is known that one of the essential building blocks of turbo codes is the interleaver and its design using random, semi-random (S-Random) and deterministic permutations. In this paper, two new types of turbo code interleavers, Modified Block S-Random (MBSR) interleaver and Modified Matched S-Random (MMSR) interleaver are proposed. The design algorithm for the new interleavers is described in depth, and the simulation results are compared to the two new interleavers with different existing interleavers based on the BER (Bit Error Rate) performances of the turbo codes. Through the simulation, we find a better performance of the MBSR interleaver than random and practical interleavers.In addition, the performance of MMSR interleaver is close to the code matched interleaver at different frame sizes and with less complex design.Index Terms-Interleaver, semi random, turbo codes, weight distribution. I. INTRODUCTIONA typical turbo code (TC) was first introduced in 1993 by Berrou et al.,[1] as a class of near channel capacity achieving codes. This turbo code is constructed by concatenating two parallel convolutional codes via an interleaver as shown in Fig. 1. The interleaver is an indexing function given by a permutation of bits index in the information frames with N frame length that plays a crucial role in the turbo codes architecture. Interleaver has three main functions: a) it constructs a long code from small memory convolutional codes by permuting the input bits such that the two constituent encoders are operating on different order input bits. b) Provides "scrambled" information data to the second constituent encoder to decorrelate the inputs of the two decoders, so that an iterative suboptimum decoding algorithm based on "uncorrelated" information exchange between the two constituent decoders can be applied. c) It changes theweight distribution of turbo codes such that, the overall weight for the generated codeword depends on how the outputs from the two constituent encoders are teamed together.The main two properties characterize any interleaver are the interleaver spreading property which is the distance between adjacent bits before interleaving, and the randomness property that provides a non-fixed indexing function which is a good factor for correction in the iterative decoding. Turbo code interleaver types have been Manuscript received May 31, 2014; revised July 17, 2014. This work was supported in part by College of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, ChinaThe authors are with the Nanjing university of Aeronautics and Astronautics, College of Electronic and Information Engineering, Nanjing (e-mail: thms78@gmail.com, saqibejaz@gmail.com).extensively studied in different ways, and they fall into two main classes: Random interleavers and Deterministic interleavers. A random interleaver is simply a random permutation with new positions produced by an indexing function based on the uniform probability distribution. While in majo...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The Design of New Modified Block and Matched S-Random Interleavers for Turbo Codes

Soliman¹,

Yang²,

Ejaz³

2014

IJMO

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“…Low-density parity-check codes [1] have acquired considerable attention due to its near-capacity error execution and powerful channel coding technique with an adequately long codeword length. The performance of LDPC codes has been investigated in [2,3], and are encountered to outperform turbo codes.…”

Section: Introductionmentioning

confidence: 99%

Lower Computation and Storage Complexity of QC-LDPC Codes in Rayleigh Fading Channel

Yahya¹,

Sidek²,

Salleh³

et al. 2009

IJCTE

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Abstract-This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes and a new multicarrier frequency hopping spread spectrum (MCFH-SS) system. The performance of newly obtained codes is evaluated by comparing with Reed Solomon (RS) codes. The computer simulation results show that the two girth-twelve QC-LDPC codes significantly outperform conventional RS codes with a gain of 2.1 dB at Index Terms-Bit error rate, DPSK, Girth, QC-LDPC, Rayleigh fading I. INTRODUCTIONA thought-provoking mission for wireless channels to communicate authentic data postulates many unusual problems. Low-density parity-check codes [1] have acquired considerable attention due to its near-capacity error execution and powerful channel coding technique with an adequately long codeword length. The performance of LDPC codes has been investigated in [2,3], and are encountered to outperform turbo codes.The potency of LDPC codes is outclass over the additive White Gaussian noise (AWGN) channel [4], where coherent detection employing phase shift keying (PSK) [5] can be carried out with carrier phase estimation. Precise phase tracking and high-quality estimation of channel state information (CSI) is required for the appropriate execution of coherent detection.The coherent detection of PSK often experiences problems while performing on Rayleigh fading channels. The reason is inaccurate CSI, due to complex channel gains variation with a passage of time, specified that LDPC codes characteristically function at a very low signal-to-noise ratio (SNR).In order to acquire accurate CSI, the authors in [6], have derived the estimates of the complex channel gain and variance of the additive noise from known pilot symbols and an estimation filter. In their work the authors have employed Turbo codes which have been detected coherently over for No channel estimation or equalization is expected if DPSK modulation is employed. Accordingly, the receiver can be more elementary and pilot symbols can be neglected at the cost of higher SNR.In [9,10], the authors have prevailed over the CSI by employing differential PSK modulation over Rayleigh fading channels with regular LDPC codes. However, the metric, which has been derived in [9], requires accurate estimates of the amplitudes of the complex channel gains, which can degrade the performance of the system if estimation falls erroneous.In [10], authors have emphasized the operation of differential detection relatively to codes themselves. They have employed LDPC codes with column weights 3 and 4, which have high computation and storage complexity. While LDPC codes with column weight j = 2, have respective advantage, since they have lower computation and storage complexity and their encoders and decoders are merer to employ. In work [9,10], authors have used differential PSK modulation but with regular LDPC codes.In this work, large girth QC-LDPC codes have been developed by deriving the basic idea from Bit-Filling (BF) and Progressive Edge-Growth algorithms proposed by C...

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“…Berrou, Glavieux and Thitimajshima [5] introduced an interleaver between the two encoders of a serial concatenation, which provides the correction of error burst from the inner encoder by the outer encoder. The result was called "turbo codes".…”

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confidence: 99%

“…The result was called "turbo codes". Turbo coding combines multiple simple codes into single powerful codes that operate close to Shannon capacity (see [5]). While their performance resembles that of random codes, the availability of iterative decoding algorithms makes the implementation of turbo codes practical (see, for example [9,10,16]).…”

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confidence: 99%

Parallel concatenated convolutional codes from linear systems theory viewpoint

Climent

Herranz

Perea

2016

Systems & Control Letters

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The aim of this work is to characterize two models of concatenated convolutional codes based on the theory of linear systems. The problem we consider can be viewed as the study of composite linear system from the classical control theory or as the interconnection from the behavioral system viewpoint. In this paper we provide an input-state-output representation of both models and introduce some conditions for such representations to be both controllable and observable. We also introduce a lower bound on their free distances and the column distances.

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Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1

Cited by 5,817 publications

References 2 publications

The Design of New Modified Block and Matched S-Random Interleavers for Turbo Codes

The Design of New Modified Block and Matched S-Random Interleavers for Turbo Codes

Lower Computation and Storage Complexity of QC-LDPC Codes in Rayleigh Fading Channel

Parallel concatenated convolutional codes from linear systems theory viewpoint

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